To tip or not to tip

Tipping points have become a buzzword in earth system science. The more popular the term becomes, the less clear its definition seems. While for some a tipping point is simply a metaphor of something changing quickly, others mean a bifurcation threshold in a strict mathematical sense. Also the Intergovernmental Panel on Climate Change has struggled defining tipping, relying on challenging notions such as abruptness and irreversibility. However, agreeing on what tipping means, and whether a system tips or not, is important both for robust science as well as for communicating climate tipping risk to policymakers and the public.

Here we critically evaluate the problems with existing tipping definitions. Based on this, we propose a revised definition that characterizes tipping behavior as a nonlinear transition in forced systems. Our definition emphasizes both the phenomenology (observed time series) and cause (feedback mechanism) of a tipping event. While compatible with dynamical systems theory, our proposition avoids concepts such as bifurcations or equilibrium states, making the definition applicable also to transient dynamics in highly complex systems under time-varying forcing. We showcase its practical use in case studies of earth system model data, comparing slow tipping systems (e.g. ice sheets) with fast tipping systems (e.g. tropical rainforests).